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Testing for symmetric correlation matrices with applications to factor models

Author

Listed:
  • Nan‐Jung Hsu
  • Lai Heng Sim
  • Ruey S. Tsay

Abstract

Factor models have been widely used in recent years to model high‐dimensional spatio‐temporal data. However, the validity of employing factor models in a specific application has received less attention. This article proposes test statistics for testing the symmetry in cross‐correlation matrices of a high‐dimensional stochastic process implied by exact factor models. A rejection of symmetry indicates that the use of an exact factor model is questionable. Both simulations and real examples are used to demonstrate the applications and to study the finite‐sample performance of the proposed test statistics. Empirical results show that the proposed test statistics are effective in identifying cases where exact factor models are not appropriate, providing valuable guidance for choosing factor models in a high‐dimensional setting.

Suggested Citation

  • Nan‐Jung Hsu & Lai Heng Sim & Ruey S. Tsay, 2023. "Testing for symmetric correlation matrices with applications to factor models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 622-643, September.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:5-6:p:622-643
    DOI: 10.1111/jtsa.12702
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    3. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    5. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    6. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    7. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    8. Tsay, Ruey S., 2020. "Testing serial correlations in high-dimensional time series via extreme value theory," Journal of Econometrics, Elsevier, vol. 216(1), pages 106-117.
    9. Guy Melard & Marianne Paesmans & Roch Roy, 1991. "Consistent Estimation Of The Asymptotic Covariance Structure Of Multivariate Serial Correlations," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(4), pages 351-361, July.
    10. T. Anderson, 1963. "The use of factor analysis in the statistical analysis of multiple time series," Psychometrika, Springer;The Psychometric Society, vol. 28(1), pages 1-25, March.
    11. Guy Melard & Marianne Paesmans & Roch Roy, 1991. "Consistent estimation of the asymptotic covariance structure of multivariate serial correlation," ULB Institutional Repository 2013/13722, ULB -- Universite Libre de Bruxelles.
    12. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
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